Suppose m and n are relatively prime positive integers. Show that the m n integers {mx +n y: 1< xSn, 1sys m} are incongruent mod m n. Show that mx+ny

is relatively prime to mn exactly when3.GCD(x,n) = GCD(y,m) = 1. Deduce from this that if m and n are relatively prime then \phi(\mathrm{m} \mathrm{n})=\phi(\mathrm{m}) \phi(\mathrm{n}), \quad \text { where } \phi(\mathrm{m}) \text { is the Euler function that counts the number of } integers relatively prime to m.